Combination of Lenses

Combination of Lenses Example

$M=M_e\cdot m_o=\frac{N}{f_e}\cdot \frac{(l-f_e)}{d_o}$

• $M$ is the overall magnification of the microscope — product of eyepiece and objective magnifications.
• $M_e$ is the eyepiece magnification. $M_e=N/f_e$
• $m_o$ is the objective magnification. $m_o=(l-f_e)/d_o$
• $N$ is the near point distance (conventional least distance of distinct vision, typically 250 mm).
• $f_e$ is the focal length of the eyepiece.
• $f_o$ is the focal length of the objective.
• $l$ is the tube length (distance between objective and eyepiece focal points).
• $d_o$ is the object distance from the objective.

When the focal lengths are much smaller than the tube length ($f_o,f_e\ll l$), the object sits approximately at $f_o$, so $d_o\approx f_o$ and $(l-f_e)\approx l$, giving the simplified form:

$M\approx -\frac{Nl}{f_e{f}_o}$

The negative sign indicates an inverted image.